Question

solve:
\frac{(x + 5)(x + 1)}{x - 4} \geq 0
? \leq x \leq or x >

Explanation:

Step1: Find critical points

Set numerator/denominator to 0:
$x+5=0 \implies x=-5$; $x+1=0 \implies x=-1$; $x-4=0 \implies x=4$

Step2: Test intervals

Test $x<-5$: $\frac{(-)(-)}{(-)}<0$
Test $-50$
Test $-1Test $x>4$: $\frac{(+)(+)}{(+)}>0$

Step3: Check critical points

$x=-5, x=-1$ make numerator 0, so satisfy $\geq0$; $x=4$ is undefined.

Answer:

$-5 \leq x \leq -1$ or $x > 4$
Filled blanks: $\boldsymbol{-5}$, $\boldsymbol{-1}$, $\boldsymbol{4}$